The uncoupled problem

In the stochastic gyre model of [FMZ97], f = 0 in eqn. (5), $g \ne 0$ in eqn. (6), the white-noise forcing N of the ocean by the wind induces a response in the strength of the intergyre gyre

$$\Psi g\vert _w \, = \, \int_{t-t_d^{ig}}^t \tau \, {\rm d} t' \, = \, \int_{t-t_d^{ig}}^t N \, {\rm d} t'$$

As the gyre fluctuates in strength, so does its meridional heat transport, thus inducing changes in SST. The impact of Q₀, eqn. (6), on the evolution of $\Delta T$, eqn. (4), then is to add a stochastic forcing term $g \int_{t-t_d^{ig}}^t N \, {\rm d} t'$ to $-\alpha N$, which reduces the power of the total stochastic forcing at low frequencies relative to the [FH77] case (cf. Fig. 6a). Despite its capability to account for observed decrease in spectral power in $\Delta T$ in the band 50-100yr, the observed enhanced power in the decadal band relative to the [FH77] case cannot be reproduced by this model. We show next, that relaxing the limiting case by allowing $f \ne 0$, i.e. acknowledging an active feedback of the ocean on the atmosphere yields a closer agreement between modelled and observed spectra.